Dual solutions of exponentially stretched/shrinked flows of nanofluids

An analysis is made of a steady two-dimensional boundary layer flow of a nanofluid and heat transfer over a stretching/shrinking sheet. The governing boundary layer equations are reduced into ordinary differential equations by a similarity transformation which are then solved numerically for three types of nanoparticles, namely copper (Cu), alumina (Al2O3), and titania (TiO2) in the water based fluid with Prandtl number Pr = 6.2. The model used for the nanofluid incorporates the effect of nanoparticles volume fraction ϕ and stretching/shrinking parameter λ. The skin friction coefficient, the local Nusselt number and the velocity and temperature profiles are presented graphically and discussed. It was found that the dual solutions exist in a certain range of the suction parameter for both stretching and shrinking cases. The nanoparticle volume fraction ϕ and the types of nanoparticles play an important role to significantly determine the flow behavior. It is also found that the range of the mass suction parameter S where the similarity solution exists for the steady two-dimensional boundary flow over an exponentially stretching/shrinking sheet is larger compared with the linear stretching/shrinking sheet case.

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